<p>The problem is: For any cube, if the volume is V cubic inches and the surface area is A square inches, then V is directly proportional to which of the following?
A A
B A^2
C A^3
D A^(2/3)
E A^(3/2)</p>
<p>The answer is E but I don't get why. This was asked before on collegeconfidential but I didn't understand the explanation. Basically, V = x^3 and A = 6(x^2); if you try to solve A for x and then plug that into V, you get (A/6)^3/2
Actually, to be honest, I don't even get what the question is saying. Why couldn't you just plug in numbers? If I plugged in 3, I would get V = 27 and SA = 54. How does that even lead to answer E? Thank you.</p>
<p>You’re on the right track. If V=(A/6)^(3/2), as you said, then you can simplify to get V=(A^(3/2))/(6^(3/2)) or V=(1/(6^(3/2)))(A^(3/2)). Sorry for all the parentheses! But what this means is that now you have V=kA^(2/3), where k is a constant: 1/(6^(3/2)). So V is directly proportional to A^(3/2) because it’s equal to A^(3/2) times a constant.</p>
<p>If you want to use the plug in numbers way, you have to use logarithms (or keep trying answer choices).</p>
<p>Suppose one side of the cube is 2. Therefore the surface area of one side is 4 (2<em>2, or 2^2), and the volume of the cube is 8 (2</em>2*2, or 2^3).</p>
<p>The problem says that the surface area can be represented by A, so in this case A = 4.</p>
<p>You can plug in 4 for A in all of those answer choices and eventually you’ll get an answer choice that works and results in the volume of the cube, 8.</p>
<p>Or, use your calculator to find the logarithm of 8, base 4, to get the desired exponent.
log(8)/log(4) = 3/2 (change of base formula)</p>
<p>In a cube, all sides are same length… so all faces are squares!</p>
<p>It says surface area is A… now to find the length we find square root of A… to find volume now we take the square root of A and multiply it by square root of A and AGAIN multiply square root of A</p>
<p>Now replace the A with any number who’s square root is a NON decimal number. I will use 16 as an example… square root of a surface area of 16 is (√16) or aka 4… now you know each side is (√16) or 4… now the volume you find of a cube is l<em>b</em>h… (√16)(√16)(√16) OR 4<em>4</em>4… 64 right</p>
<p>so proportions between A to V</p>
<p>A = 16
V = 64</p>
<p>A^x = V
16^x=64</p>
<p>solving for x gives 1.5 or 3/2!</p>
<p>you can use any square number like 9,16,25,36,49,64,81 and on and on. </p>
<p>Reposted my answer from another one of my post under similar question haha, because you asked the same question as the other guy! :P</p>